Multi-signature schemes in pairing-free settings require multiple communication rounds, prompting efforts to reduce the number of signing rounds that need to be executed after the signers receive the message to sign. In MuSig and Bellare-Neven multi-signatures, the signing protocol does not use the message until the third (and final) signing round. This structure seemingly allows pre-processing of the first two signing rounds before the signers receive the message. However, we demonstrate...

Since its introduction by Wagner (CRYPTO `02), the $k$-list algorithm has found significant utility in cryptanalysis. One important application thereof is in computing forgeries on several interactive signature schemes that implicitly rely on the hardness of the ROS problem formulated by Schnorr (ICICS `01). The current best attack strategy for these schemes relies the conjectured runtime of the $k$-list algorithm over $\mathbb{Z}_p$. The tightest known analysis of Wagner's algorithm over...

Many of the three-round blind signatures based on identification protocols are only proven to be $\ell$-concurrently unforgeable for $\ell = \mathsf{polylog}(\lambda)$. It was only recently shown in a seminal work by Benhamouda et al. (EUROCRYPT'21) that this is not just a limitation of the proof technique. They proposed an elegant polynomial time attack against the $\ell$-concurrently unforgeability of the classical blind Schnorr protocol for $\ell = \mathsf{poly}(\lambda)$. However,...

Blind signatures allow the issuing of signatures on messages chosen by the user so that they ensure $\mathit{blindness}$ of the message against the signer. Moreover, a malicious user cannot output $\ell+1$ signatures while only finishing $\ell$ signing sessions. This notion, called $\mathit{one}$-$\mathit{more}$ unforgeability, comes in two flavors supporting either $\mathit{sequential}$ or $\mathit{concurrent}$ sessions. In this paper, we investigate the security of a class of blind...

In this paper, we construct the first provably-secure isogeny-based (partially) blind signature scheme. While at a high level the scheme resembles the Schnorr blind signature, our work does not directly follow from that construction, since isogenies do not offer as rich an algebraic structure. Specifically, our protocol does not fit into the "linear identification protocol" abstraction introduced by Hauck, Kiltz, and Loss (EUROCYRPT'19), which was used to generically construct...

This paper proposes the first practical pairing-free three-move blind signature schemes that (1) are concurrently secure, (2) produce short signatures (i.e., three or four group elements/scalars), and (3) are provably secure either in the generic group model (GGM) or the algebraic group model (AGM) under the (plain or one-more) discrete logarithm assumption (beyond additionally assuming random oracles). We also propose a partially blind version of one of our schemes. Our schemes do not rely...

In this paper, we give the first formal security analysis on the one-more unforgeability of blind ECDSA. We start with giving a general attack on blind ECDSA, which is similar to the ROS attack on the blind Schnorr signature. We formulate the ECDSA-ROS problem to capture this attack. Next, we give a generic construction of blind ECDSA based on an additive homomorphic encryption and a corresponding zero-knowledge proof. Our concrete instantiation is about 40 times more bandwidth efficient...

We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem in polynomial time for l > log p dimensions. Our algorithm can be combined with Wagner’s attack, and leads to a sub-exponential solution for any dimension l with best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto--Schnorr blind...

The Schnorr blind signing protocol allows blind issuing of Schnorr signatures, one of the most widely used signatures. Despite its practical relevance, its security analysis is unsatisfactory. The only known security proof is rather informal and in the combination of the generic group model (GGM) and the random oracle model (ROM) assuming that the ``ROS problem'' is hard. The situation is similar for (Schnorr-)signed ElGamal encryption, a simple CCA2-secure variant of ElGamal. We analyze...

This paper proposes a new scheme for partially blind signature based on the difficulty in solving the discrete logarithm problem. Under the assumption of the generic model, random oracle model, and intractable ROS-problem, this paper formally proves that the proposed scheme is secure against one-more signature forgery under the adaptively parallel attack. Previous schemes using two signing equations for plain information and commitment. The proposed scheme uses two secret keys to combine...

We present the first blind identity-based signcryption (BIBSC). We formulate its security model and define the security notions of blindness and parallel one-more unforgeability (p1m-uf). We present an efficient construction from pairings, then prove a security theorem that reduces its p1m-uf to Schnorr¡¦s ROS Problem in the random oracle model plus the generic group and pairing model. The latter model is an extension of the generic group model to add support for pairings, which we introduce...